
where \(\beta _i\)  is a generic increasing utility function of the data rate \(c_i\)  [cf. (REF )], and \(p_{\max }\)  denotes the uniform maximum available power at every transmitter.
Notice that when selecting \(\beta _i(z) = \alpha _i z\)  for \(\alpha _i>0\) , the objective function in (REF ) boils down to the well-established (weighted) sum-rate utility.
Moreover, other frequently encountered utilities are also encompassed by the formulation in (REF ) including proportional fairness \(\beta _i(z) = \log (z)\)  and harmonic mean rate \(\beta _i(z) = -z^{-1}\) .
However, even for well-established utility functions, the optimization problem in (REF ) has been shown to be NP-hard [1]}, [2]}.
In this context, the present work is driven by the following question:
